Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
1.6 kgk = ?

A 1.6 kg mass on a spring oscillates with a period of 0.4 s. Find the spring stiffness k.

m = 1.6 kgT = 0.4 s
k = N/m
2.Easy
3.5 kgk = 170 N/m

A 3.5 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.5 kgk = 170 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
4.Medium
2 kgk = 80 N/mA = 9 cmx = 5 cm

A 2 kg mass on a spring with k = 80 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 5 cm from equilibrium.

m = 2 kgk = 80 N/mA = 9 cmx = 5 cm
v = m/s
5.Hard
1.8 kgk = 70 N/mA = 16 cm

A 1.8 kg mass on a spring with k = 70 N/m is pulled 16 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 70 N/mA = 16 cm
E = J
6.Hard
2.3 kgk = 120 N/mA = 7 cm

A 2.3 kg mass on a spring with k = 120 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.3 kgk = 120 N/mA = 7 cm
vmax = m/s

Answer key

  1. 1. k = 394.8 N/m
  2. 2. f = 1.109 Hz
  3. 3. L = 0.3007 m
  4. 4. v = 0.4733 m/s
  5. 5. E = 0.896 J
  6. 6. vmax = 0.5056 m/s

Full step-by-step solutions: practise this topic on examproblems.com.